If you need instructions on how to build *ELPA*, please look at [INSTALL.md] (INSTALL.md).

### Online and local documentation ###

Local documentation (via man pages) should be available (if *ELPA* has been installed with the documentation):

For example "man elpa2_print_kernels" should provide the documentation for the *ELPA* program which prints all

For example "man elpa2_print_kernels" should provide the documentation for the *ELPA* program, which prints all

the available kernels.

Also a [online doxygen documentation] (http://elpa.mpcdf.mpg.de/html/Documentation/ELPA-2018.05.001.rc1/html/index.html)

for each *ELPA* release is available.

## API of the *ELPA* library ##

### API of the *ELPA* library ###

With release 2017.05.001 of the *ELPA* library the interface has been rewritten substantially, in order to have a more generic interface and to avoid future interface changes.

With release 2017.05.001 of the *ELPA* library the interface has been rewritten substantially, in order to have a more generic

interface and to avoid future interface changes.

For compatibility reasons the interface defined in the previous release 2016.11.001 is also still available

IF AND ONLY IF *ELPA* has been build with support of this legacy interface.

If you want to use the legacy interface, please look to section "B) Using the legacy API of the *ELPA* library.

**IF AND ONLY IF***ELPA* has been build with support of this legacy interface.

The legacy API defines all the functionality as it has been defined in *ELPA* release 2016.11.011. Note, however,

that all future features of *ELPA* will only be accessible via the new API defined in release 2017.05.001 or later.

## A) Using the final API definition of the *ELPA* library ##

As mentioned, we advise against it, but if you want to use the legacy API please look at the document

- V) Influencing default values with environment variables

- VI) Autotuning

## I) General concept of the *ELPA* API ##

Using *ELPA*with the latest API is done in the following steps

Using *ELPA*just requires a few steps:

- include elpa headers "elpa/elpa.h" (C-Case) or use the Fortran module "use elpa"

...

...

@@ -45,469 +60,302 @@ Using *ELPA* with the latest API is done in the following steps

- set or get all possible ELPA tunable options with ELPA-type functions get/set

At the moment the following tunable options are available:

- "solver" can either be ELPA_SOLVER_1STAGE or ELPA_SOLVER_2STAGE

- "real_kernel" can be one of the available real kernels (a list of available kernels can be

queried with the ELPA helper binary elpa2_print_kernels)

- "complex_kernel" can be one of the available complex kernels (a list of available kernels can be

- "qr" can be either 0 or 1, switches QR decomposition off/on for ELPA_SOLVER_2STAGE

only available in real-case for blocksize at least 64

- "gpu" can be either 0 or 1, switches GPU computations off or on, assuming that the installation

of the ELPA library has been build with GPU support enables

- "timings" can be either 0 or 1, switches time measurements off or on

- "debug" can be either 0 or 1, switches detailed debug messages off/on

- call ELPA-type function solve or others

At the moment the following ELPA compute functions are available:

- "eigenvectors" solves the eigenvalue problem for single/double real/complex valued matrices and

returns the eigenvalues AND eigenvectors

- "eigenvalues" solves the eigenvalue problem for single/double real/complex valued matrices and

returns the eigenvalues

- "hermetian_multipy" computes C = A^T * B (real) or C = A^H * B (complex) for single/double

real/complex matrices

- "cholesky" does a cholesky factorization for a single/double real/complex matrix

- "invert_triangular" inverts a single/double real/complex triangular matrix

- "solve_tridiagonal" solves the single/double eigenvalue problem for a real tridiagonal matrix

- if the ELPA object is not needed any more call ELPA-type function destroy

- call elpa_uninit at the end of the program

## B) Using the legacy API of the *ELPA* library ##

The following description describes the usage of the *ELPA* library with the legacy interface.

### General concept of the *ELPA* library ###

The *ELPA* library consists of two main parts:

-*ELPA 1stage* solver

-*ELPA 2stage* solver

Both variants of the *ELPA* solvers are available for real or complex singe and double precision valued matrices.

Thus *ELPA* provides the following user functions (see man pages or [online] (http://elpa.mpcdf.mpg.de/html/Documentation/ELPA-2018.05.001.rc1/html/index.html) for details):

- elpa_get_communicators : set the row / column communicators for *ELPA*

- elpa_solve_evp_complex_1stage_{single|double} : solve a {single|double} precision complex eigenvalue proplem with the *ELPA 1stage* solver

- elpa_solve_evp_real_1stage_{single|double} : solve a {single|double} precision real eigenvalue proplem with the *ELPA 1stage* solver

- elpa_solve_evp_complex_2stage_{single|double} : solve a {single|double} precision complex eigenvalue proplem with the *ELPA 2stage* solver

- elpa_solve_evp_real_2stage_{single|double} : solve a {single|double} precision real eigenvalue proplem with the *ELPA 2stage* solver

- elpa_solve_evp_real_{single|double} : driver for the {single|double} precision real *ELPA 1stage* or *ELPA 2stage* solver

- elpa_solve_evp_complex_{single|double} : driver for the {single|double} precision complex *ELPA 1stage* or *ELPA 2stage* solver

Furthermore *ELPA* provides the utility binary "elpa2_print_available_kernels": it tells the user

which *ELPA 2stage* compute kernels have been installed and which default kernels are set

If you want to solve an eigenvalue problem with *ELPA*, you have to decide whether you

want to use *ELPA 1stage* or *ELPA 2stage* solver. Normally, *ELPA 2stage* is the better

choice since it is faster, but there are matrix dimensions where *ELPA 1stage* is superior.

Independent of the choice of the solver, the concept of calling *ELPA* is always the same:

#### MPI version of *ELPA* ####

In this case, *ELPA* relies on a BLACS distributed matrix.

To solve a Eigenvalue problem of this matrix with *ELPA*, one has

1. to include the *ELPA* header (C case) or module (Fortran)

2. to create row and column MPI communicators for ELPA (with "elpa_get_communicators")

3. to call to the *ELPA driver* or directly call *ELPA 1stage* or *ELPA 2stage* for the matrix.

Here is a very simple MPI code snippet for using *ELPA 1stage*: For the definition of all variables

please have a look at the man pages and/or the online documentation (see above). A full version

of a simple example program can be found in ./test_project_1stage_legacy_api/src.

! All ELPA routines need MPI communicators for communicating within

! rows or columns of processes, these are set in elpa_get_communicators

With the definintions of the input and output variables:

integer, intent(in) na: global dimension of quadratic matrix a to solve

integer, intent(in) nev: number of eigenvalues to be computed; the first nev eigenvalules are calculated

real*{4|8}, intent(inout) a: locally distributed part of the matrix a. The local dimensions are lda x matrixCols

integer, intent(in) lda: leading dimension of locally distributed matrix a

real*{4|8}, intent(inout) ev: on output the first nev computed eigenvalues

real*{4|8}, intent(inout) q: on output the first nev computed eigenvectors

integer, intent(in) ldq: leading dimension of matrix q which stores the eigenvectors

integer, intent(in) nblk: blocksize of block cyclic distributin, must be the same in both directions

integer, intent(in) matrixCols: number of columns of locally distributed matrices a and q

integer, intent(in) mpi_comm_rows: communicator for communication in rows. Constructed with elpa_get_communicators(3)

integer, intent(in) mpi_comm_cols: communicator for communication in colums. Constructed with elpa_get_communicators(3)

logical success: return value indicating success or failure

C INTERFACE

#include "elpa.h"

success = elpa_solve_evp_real_1stage_{single|double} (int na, int nev, double *a, int lda, double *ev, double *q, int ldq, int nblk, int matrixCols, int

mpi_comm_rows, int mpi_comm_cols);

With the definintions of the input and output variables:

int na: global dimension of quadratic matrix a to solve

int nev: number of eigenvalues to be computed; the first nev eigenvalules are calculated

{float|double} *a: pointer to locally distributed part of the matrix a. The local dimensions are lda x matrixCols

int lda: leading dimension of locally distributed matrix a

{float|double} *ev: pointer to memory containing on output the first nev computed eigenvalues

{float|double} *q: pointer to memory containing on output the first nev computed eigenvectors

int ldq: leading dimension of matrix q which stores the eigenvectors

int nblk: blocksize of block cyclic distributin, must be the same in both directions

int matrixCols: number of columns of locally distributed matrices a and q

int mpi_comm_rows: communicator for communication in rows. Constructed with elpa_get_communicators(3)

int mpi_comm_cols: communicator for communication in colums. Constructed with elpa_get_communicators(3)

int success: return value indicating success (1) or failure (0)

DESCRIPTION

Solve the real eigenvalue problem with the 1-stage solver. The ELPA communicators mpi_comm_rows and mpi_comm_cols are obtained with the

elpa_get_communicators(3) function. The distributed quadratic marix a has global dimensions na x na, and a local size lda x matrixCols.

The solver will compute the first nev eigenvalues, which will be stored on exit in ev. The eigenvectors corresponding to the eigenvalues

will be stored in q. All memory of the arguments must be allocated outside the call to the solver.

With the definintions of the input and output variables:

integer, intent(in) na: global dimension of quadratic matrix a to solve

integer, intent(in) nev: number of eigenvalues to be computed; the first nev eigenvalules are calculated

complex*{8|16}, intent(inout) a: locally distributed part of the matrix a. The local dimensions are lda x matrixCols

integer, intent(in) lda: leading dimension of locally distributed matrix a

real*{4|8}, intent(inout) ev: on output the first nev computed eigenvalues

complex*{8|16}, intent(inout) q: on output the first nev computed eigenvectors

integer, intent(in) ldq: leading dimension of matrix q which stores the eigenvectors

integer, intent(in) nblk: blocksize of block cyclic distributin, must be the same in both directions

integer, intent(in) matrixCols: number of columns of locally distributed matrices a and q

integer, intent(in) mpi_comm_rows: communicator for communication in rows. Constructed with elpa_get_communicators(3)

integer, intent(in) mpi_comm_cols: communicator for communication in colums. Constructed with elpa_get_communicators(3)

logical success: return value indicating success or failure

C INTERFACE

#include "elpa.h"

#include <complex.h>

success = elpa_solve_evp_complex_1stage_{single|double} (int na, int nev, double complex *a, int lda, double *ev, double complex*q, int ldq, int nblk, int

matrixCols, int mpi_comm_rows, int mpi_comm_cols);

With the definintions of the input and output variables:

int na: global dimension of quadratic matrix a to solve

int nev: number of eigenvalues to be computed; the first nev eigenvalules are calculated

{float|double} complex *a: pointer to locally distributed part of the matrix a. The local dimensions are lda x matrixCols

int lda: leading dimension of locally distributed matrix a

{float|double} *ev: pointer to memory containing on output the first nev computed eigenvalues

{float|double} complex *q: pointer to memory containing on output the first nev computed eigenvectors

int ldq: leading dimension of matrix q which stores the eigenvectors

int nblk: blocksize of block cyclic distributin, must be the same in both directions

int matrixCols: number of columns of locally distributed matrices a and q

int mpi_comm_rows: communicator for communication in rows. Constructed with elpa_get_communicators(3)

int mpi_comm_cols: communicator for communication in colums. Constructed with elpa_get_communicators(3)

int success: return value indicating success (1) or failure (0)

DESCRIPTION

Solve the complex eigenvalue problem with the 1-stage solver. The ELPA communicators mpi_comm_rows and mpi_comm_cols are obtained with the

elpa_get_communicators(3) function. The distributed quadratic marix a has global dimensions na x na, and a local size lda x matrixCols.

The solver will compute the first nev eigenvalues, which will be stored on exit in ev. The eigenvectors corresponding to the eigenvalues

will be stored in q. All memory of the arguments must be allocated outside the call to the solver.

The *ELPA 1stage* solver, does not need or accept any other parameters than in the above

specification.

#### Using *ELPA 2stage* ####

The *ELPA 2stage* solver can be used in the same manner, as the *ELPA 1stage* solver.

However, the 2 stage solver, can be used with different compute kernels, which offers

more possibilities for configuration.

It is recommended to first call the utility program

elpa2_print_kernels

which will tell all the compute kernels that can be used with *ELPA 2stage*". It will

also give information, whether a kernel can be set via environment variables.

##### Using the default kernels #####

If no kernel is set either via an environment variable or the *ELPA 2stage API* then

the default kernels will be set.

To be more precise a basic call sequence for Fortran and C looks as follows:

Fortran synopsis

```Fortran

use elpa

class(elpa_t), pointer :: elpa

integer :: success

##### Setting the *ELPA 2stage* compute kernels #####

if (elpa_init(20171201) /= ELPA_OK) then ! put here the API version that you are using

print *, "ELPA API version not supported"

stop

endif

elpa => elpa_allocate()

! set parameters decribing the matrix and it's MPI distribution

call elpa%set("na", na, success) ! size of the na x na matrix

call elpa%set("nev", nev, success) ! number of eigenvectors that should be computed ( 1<= nev <= na)

call elpa%set("local_nrows", na_rows, success) ! number of local rows of the distributed matrix on this MPI task

call elpa%set("local_ncols", na_cols, success) ! number of local columns of the distributed matrix on this MPI task

call elpa%set("nblk", nblk, success) ! size of the BLACS block cyclic distribution

call elpa%set("mpi_comm_parent", MPI_COMM_WORLD, success) ! the global MPI communicator

call elpa%set("process_row", my_prow, success) ! row coordinate of MPI process

call elpa%set("process_col", my_pcol, success) ! column coordinate of MPI process

##### Setting the *ELPA 2stage* compute kernels with environment variables#####

succes = elpa%setup()

If the *ELPA* installation allows setting their compute kernels with environment variables,

setting the variables "REAL_ELPA_KERNEL" and "COMPLEX_ELPA_KERNEL" will set the compute

kernels. The environment variable setting will take precedence over all other settings!

! if desired, set any number of tunable run-time options

! look at the list of possible options as detailed later in

! USERS_GUIDE.md

call e%set("solver", ELPA_SOLVER_2STAGE, success)

The utility program "elpa2_print_kernels" can list which kernels are available and which

would be chosen. This reflects the setting of the default kernel as well as the setting

with the environment variables.

! use method solve to solve the eigenvalue problem to obtain eigenvalues

! and eigenvectors

! other possible methods are desribed in USERS_GUIDE.md

call e%eigenvectors(a, ev, z, success)

##### Setting the *ELPA 2stage* compute kernels with API calls#####

! cleanup

call elpa_deallocate(e)

It is also possible to set the *ELPA 2stage* compute kernels via the API.

call elpa_uninit()

```

As an example the API for ELPA real double-precision 2stage is shown:

int na: global dimension of quadratic matrix a to solve

int nev: number of eigenvalues to be computed; the first nev eigenvalules are calculated

double *a: pointer to locally distributed part of the matrix a. The local dimensions are lda x matrixCols

int lda: leading dimension of locally distributed matrix a

double *ev: pointer to memory containing on output the first nev computed eigenvalues

double *q: pointer to memory containing on output the first nev computed eigenvectors

int ldq: leading dimension of matrix q which stores the eigenvectors

int nblk: blocksize of block cyclic distributin, must be the same in both directions

int matrixCols: number of columns of locally distributed matrices a and q

int mpi_comm_rows: communicator for communication in rows. Constructed with elpa_get_communicators(3)

int mpi_comm_cols: communicator for communication in colums. Constructed with elpa_get_communicators(3)

int mpi_comm_all: communicator for all processes in the processor set involved in ELPA

int useQR: if set to 1 switch to QR-decomposition

int useGPU: decide whether the GPU version should be used or not

/* use method solve to solve the eigenvalue problem */

/* other possible methods are desribed in USERS_GUIDE.md */

elpa_eigenvectors(handle, a, ev, z, &error);

int success: return value indicating success (1) or failure (0)

/* cleanup */

elpa_deallocate(handle);

elpa_uninit();

```

## II) List of supported tunable parameters ##

DESCRIPTION

Solve the real eigenvalue problem with the 2-stage solver. The ELPA communicators mpi_comm_rows and mpi_comm_cols are obtained with the

elpa_get_communicators(3) function. The distributed quadratic marix a has global dimensions na x na, and a local size lda x matrixCols.

The solver will compute the first nev eigenvalues, which will be stored on exit in ev. The eigenvectors corresponding to the eigenvalues

will be stored in q. All memory of the arguments must be allocated outside the call to the solver.

The following table gives a list of all supported parameters which can be used to tune (influence) the runtime behaviour of *ELPA* ([see here if you cannot read it in your editor] (https://gitlab.mpcdf.mpg.de/elpa/elpa/wikis/USERS_GUIDE))

##### Setting up *ELPA 1stage* or *ELPA 2stage* with the *ELPA driver interface* #####

| Parameter name | Short description | default value | possible values | since API version |

| gpu | use GPU (if build <br> with GPU support)| 0 | 0 or 1 | 20170403 |

| real_kernel | real kernel to be <br> used in ELPA 2 | ELPA_2STAGE_REAL_DEFAULT | see output of <br> elpa2_print_kernels | 20170403 |

| complex kernel | complex kernel to <br> be used in ELPA 2 | ELPA_2STAGE_COMPLEX_DEFAULT | see output of <br> elpa2_print_kernels | 20170403 |

| omp_threads | OpenMP threads used <br> (if build with OpenMP <br> support) | 1 | >1 | 20180525 |

| qr | Use QR decomposition in <br> ELPA 2 real | 0 | 0 or 1 | 20170403 |

| timings | Enable time <br> measurement | 1 | 0 or 1 | 20170403 |

| debug | give debug information | 0 | 0 or 1 | 20170403 |

Since release ELPA 2016.005.004 a driver routine allows to choose more easily which solver (1stage or 2stage) will be used.

## III) List of computational routines ##

As an exmple the real double-precision case is explained:

The following compute routines are available in *ELPA*: Please have a look at the man pages or [online doxygen documentation] (http://elpa.mpcdf.mpg.de/html/Documentation/ELPA-2018.05.001.rc1/html/index.html) for details.

Generalized interface to the ELPA 1stage and 2stage solver for real-valued problems

If *ELPA* has been build with OpenMP threading support you can specify the number of OpenMP threads that *ELPA* will use internally.

Please note that it is **mandatory** to set the number of threads to be used with the OMP_NUM_THREADS environment variable **and**

with the **set method**

With the definintions of the input and output variables:

```Fortran

call e%set("omp_threads", 4, error)

```

**or the *ELPA* environment variable**

integer, intent(in) na: global dimension of quadratic matrix a to solve

export ELPA_DEFAULT_omp_threads=4 (see Section V for an explanation of this variable).

integer, intent(in) nev: number of eigenvalues to be computed; the first nev eigenvalules are calculated

Just setting the environment variable OMP_NUM_THREADS is **not** sufficient.

real*8, intent(inout) a: locally distributed part of the matrix a. The local dimensions are lda x matrixCols

This is necessary to make the threading an autotunable option.

integer, intent(in) lda: leading dimension of locally distributed matrix a

## V) Influencing default values with environment variables ##

real*8, intent(inout) ev: on output the first nev computed eigenvalues"

For each tunable parameter mentioned in Section II, there exists a default value. This means, that if this parameter is **not explicitly** set by the user by the

*ELPA* set method, *ELPA* takes the default value for the parameter. E.g. if the user does not set a solver method, than *ELPA* will take the default "ELPA_SOLVER_1STAGE".

real*8, intent(inout) q: on output the first nev computed eigenvectors"

The user can change this default value by setting an enviroment variable to the desired value.

integer, intent(in) ldq: leading dimension of matrix q which stores the eigenvectors

The name of this variable is always constructed in the following way:

```

ELPA_DEFAULT_tunable_parameter_name=value

```

integer, intent(in) nblk: blocksize of block cyclic distributin, must be the same in both directions

, e.g. in case of the solver the user can

integer, intent(in) matrixCols: number of columns of locally distributed matrices a and q

```

export ELPA_DEFAULT_solver=ELPA_SOLVER_2STAGE

```

integer, intent(in) mpi_comm_rows: communicator for communication in rows. Constructed with elpa_get_communicators

in order to define the 2stage solver as the default.

integer, intent(in) mpi_comm_cols: communicator for communication in colums. Constructed with elpa_get_communicators

**Important note**

The default valule is completly ignored, if the user has manually set a parameter-value pair with the *ELPA* set method!

Thus the above environemnt variable will **not** have an effect, if the user code contains a line

```Fortran

call e%set("solver",ELPA_SOLVER_1STAGE,error)

```

.

integer, intent(in) mpi_comm_all: communicator for all processes in the processor set involved in ELPA

## VI) Using autotuning ##

integer, intent(in), optional: THIS_REAL_ELPA_KERNEL: optional argument, choose the compute kernel for 2-stage solver

Since API version 20171201 *ELPA* supports the autotuning of some "tunable" parameters (see Section II). The idea is that if *ELPA* is called multiple times (like typical in

self-consistent-iterations) some parameters can be tuned to an optimal value, which is hard to set for the user. Note, that not every parameter mentioned in Section II can actually be tuned with the autotuning. At the moment, only the parameters mentioned in the table below are affected by autotuning.

logical, intent(in), optional: useQR: optional argument; switches to QR-decomposition if set to .true.

There are two ways, how the user can influence the autotuning steps:

logical, intent(in), optional: useQPU: decide whether the GPU version should be used or not

1.) the user can set one of the following autotuning levels

- ELPA_AUTOTUNE_FAST

- ELPA_AUTOTUNE_MEDIUM

character(*), optional method: use 1stage solver if "1stage", use 2stage solver if "2stage", (at the moment) use 2stage solver if "auto"

Each level defines a different set of tunable parameter. The autouning option will be extended by future releases of the *ELPA* library, at the moment the following

sets are supported:

logical success: return value indicating success or failure

2.) the user can **remove** tunable parameters from the list of autotuning possibilites by explicetly setting this parameter,

e.g. if the user sets in his code

#include "elpa.h"

```Fortran

call e%set("solver", ELPA_SOLVER_2STAGE, error)

```

**before** invoking the autotuning, then the solver is fixed and not considered anymore for autotuning. Thus the ELPA_SOLVER_1STAGE would be skipped and, consequently, all possible autotuning parameters, which depend on ELPA_SOLVER_1STAGE.

success = elpa_solve_evp_real_double (int na, int nev, double *a, int lda, double *ev, double *q, int ldq, int nblk, int matrixCols, int mpi_comm_rows, int mpi_comm_cols, int mpi_comm_all, int THIS_ELPA_REAL_KERNEL, int useQR, int useGPU, char *method);"

The user can invoke autotuning in the following way:

With the definintions of the input and output variables:"

Fortran synopsis

```Fortran

! prepare elpa as you are used to (see Section I)

! only steps for autotuning are commentd

use elpa

class(elpa_t), pointer :: elpa

class(elpa_autotune_t), pointer :: tune_state ! create an autotuning pointer

integer :: success

int na: global dimension of quadratic matrix a to solve

if (elpa_init(20171201) /= ELPA_OK) then

print *, "ELPA API version not supported"

stop

endif

elpa => elpa_allocate()

int nev: number of eigenvalues to be computed; the first nev eigenvalules are calculated

! set parameters decribing the matrix and it's MPI distribution